a) Specify the locations of poles and zeros and write the transfer function G(s).[5]b) Calculate the angle of departure (from poles)? (note: k=0, pm1, pm2,... in the angle condition of root locus). [5]c) Form the closed loop transfer function and then using Routh table find the jo-axis crossing coordinates and corresponding K? [10]d) Given the break-in coordinate of -2.43, sketch root locus. [5]

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Afour cylinder four-stroke in-line engine has a stroke of 160mm, connecting rod length of 150mm, a reciprocating mass of 3kg and its firing order is 1-3-4-2. the spacing between cylinders is 100mm. i. show that the engine is in balance with regard to the primary inertia forces and primary 3. a and secondary inertia couples. li determine the out of balance secondary inertia force ii. propose ways of balancing this out of balance force and discuss the challenges that will arise

For a gate width of 2 m into the paper, determine the force required to hold the gate abc at its location.